Number of routes

How many routes are there from the lower left corner to the upper right corner of an m*n grid if we are restricted to traveling only to the right or up? For example, in a 1*1 grid,
only two routes exist : right,up or up,right.

How many routes are there from the lower left corner to the upper right corner of an m*n grid if we are restricted to traveling only to the right or up? For example, in a 1*1 grid,
only two routes exist : right,up or up,right.

Let U stand for moving up one grid mark and R is right one.
Now to make the trip we must use m R's and n U's., how many ways can we rearrange that string?